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高中数学必修一集合的含义及其表示教案

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the principl e of simplified E IA of constr uction pr oject s in the regi on. In terms of land, li nked to t he impleme ntation of urba n and rural constr ucti on la nd i ncreas e and de crease, re placement indicat ors for pri ority areas pr oject. Charges , into t he projects of water, ele ctricit y, admini strative charges a nd preferential poli cies. I n the area of taxat ion, and settle d in areas of industry and its pr oduction company, withi n 5 years after the compl etion of fiscal incentive s to enter prises . In terms of financi ng, integrati on of la nd, tax, fina ncial a nd other res our ces, a nd construct "G overnme nt credit + busi ne ss credit" credit system, esta blishme nt of marketization, commer cialization and modernizati on of the investment a nd financing platform; effective Bank -enter prise docki ng, e ncourages private capital into the Park, to rais e industry development fund. 5, optimize t he envir onment a nd s ervice i ndus tries. To create "poli cy lowl ands, Hig hlands, i ntegrity of service land, devel opme nt land" as the goal , to optimize the area under devel opme nt environment. All a dministrative law e nforceme nt de partments to a ppoint a full -time pers onnel stationed i n areas dedi cated to coordinating and s olving pr oblems a ssociated wit h busi nesse s in thi s se ctor. When ther e are substantial i ssues, se ctor lea ders arranged to personally interve ne, i n-person, in-person push ta ngibl e area buildi ng a green lig ht, easy line . To furt her reduce a nd sta ndar dize a dministrative examination and approval items, sim plify examination a nd a ppr oval links, im prove efficie ncy; a ccordi ng to the .. . Since the educati onal practi ce of the mass line of the part y, himself s eriously in t he educati on, practical control central " eight rule s" and oppos ing "the four winds" and practi cing "three S uns", a nd che ck the spirit of Jiao Y ulu, i deol ogy, soli cit opini ons base d on out standi ng pr oblems che cked s w ing, careful a nalysi s and reflection. Will now che ck report is as foll ows: first, a dher ence to the party's political dis cipli ne, eig ht in the central provisi on, cha nge the styl e of the ba sic situation of 1, i n com pliance wit h the party' s politi cal di sci pline s. Conscienti ously abi de by the party's politica l disci pline, abi de by t he Constit ution a nd t he rule s and regulati ons of the part y, in the po litical, i deol ogical and mai ntain highly consistent wit h the CPC Central Committee on t he acti on, t here is no vi olation of the party's politi cal di sci pline problems. 2 , in the im plementati on of the central a uthori ties of the eight provisi ons. Improvi ng resear ch, im proving res earch methods, but there ar e less gras s-roots units, primary first-hand an i nadequate grasp of the problem, w hich is to be strengthene d in the future. Se cond, construction, strictly i n accorda nce with the provi sions to streamli ne and im prove the quality of meetings of the Conference. Thir d, streamlini ng file briefs, cult ure involve s all aspe cts of propaganda and ide olog y, sometimes due to the practical nee ds of inve ntion notificati ons, this are a nee ds further

第一章 1.1 集合 1.1.1

集合与函数概念 集合的含义及其表示

教学目的: (1)初步理解集合的概念,知道常用数集及其记法; (2)初步了解“属于”关系的意义; (3)初步了解有限集、无限集、空集的意义; 教学重点:集合的含义与表示方法; 教学难点:运用集合的两种常用表示方法——列举法与描述法,正确表示一些简单的集合。 教学过程: 一、问题引入: 我家有爸爸、妈妈和我; 我来自燕山中学; 省溧中高一(1)班; 我国的直辖市。 分析、归纳上述各个实例的共同特征,归纳出集合的含义。 二、建构数学: 1.集合的概念:一般地,一定范围内某些确定的、不同的对象的全体构成一个集合(set) 。集合常用 大写的拉丁字母来表示,如集合 A、集合 B…… 集合中的每一个对象称为该集合的元素(element),简称元。集合的元素常用小写的拉丁字母来表 示。如 a、b、c、p、q…… 指出下列对象是否构成集合,如果是,指出该集合的元素。 (1)我国的直辖市; (2)省溧中高一(1)班全体学生; (3)较大的数 (4)young 中的字母; (5)大于 100 的数; (6)小于 0 的正数。 2.关于集合的元素的特征 (1)确定性:设 A 是一个给定的集合,x 是某一个具体对象,则或者是 A 的元素,或者不是 A 的元素,两种情况必有一种且只有一种成立。 (2)互异性:一个给定集合中的元素,指属于这个集合的互不相同的个体(对象) ,因此,同 一集合中不应重复出现同一元素。 (3)无序性:一般不考虑元素之间的顺序,但在表示数列之类的特殊集合时,通常按照习惯 的由小到大的数轴顺序书写。
3.集合元素与集合的关系用“属于”和“不属于”表示; (1)如果 a 是集合 A 的元素,就说 a 属于 A ,记作 a ∈ A (2)如果 a 不是集合 A 的元素,就说 a 不属于 A ,记作 a ? A ( “∈”的开口方向,不能把 a∈A 颠倒过来写 )
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4.有限集、无限集和空集的概念:
5.常用数集的记法: (1)非负整数集(自然数集) :全体非负整数的集合 记作 N, N ? ?0,1,2, ??
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(2)正整数集:非负整数集内排除 0 的集 记作 N*或 N+
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N* ?? 1,2,3, ??

? 1, ? 2, ?? (3)整数集:全体整数的集合 记作 Z , Z ? ?0,
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(4)有理数集:全体有理数的集合 记作 Q ,
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? Q ? ?整数与分数
(5)实数集:全体实数的集合 记作 R
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?的 R ?? 数 轴 上 所 有 点 所 对数 应
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注: (1)自然数集与非负整数集是相同的,也就是说,自然数集包括数 0
streamlining. Four are sta ndar d visits, exce pt as re quire d to parti cipate i n training , no other a ctivity. Five is to im prove ne ws reporting , for propaganda work stri ctly accor ding to t he regulati ons . Six is strictly y our pre sentati on publ ishe d strictly a ccordi ng to the reg ulations. 罚 济 经 或 决 理 处 好 做 权 作 操 规 违 承 对 。 明 文 与 全 安 、 度 进 督 监 并 , 宜 事 关 有 的 中 工 施 调 协 责 负 专 定 指 人 包 发 Seven is strictly thrift, require d the use of ve hicle s and office s pace and cor porate hos pitality. 3, change t he style.

Propaganda a nd i deological work of the new situati on a nd new requirements of the new tasks, had done a lot of fruitful work, ha s made many a chi evements, but further cl oser to t he grass r oots, close to realit y, cl ose to t he masse s and als o ina dequate innovati on must continue to impr ove. Second, the "four winds" some outsta ndi ng iss ues 1 , oppose formalism. One t heory i s that he didn't, with le ss clos e contact. T he oretical st udy of consci ousne ss is not hig h enoug h, system performance is not strong enoug h; more passive le arni ng, active le arni ng few generalities a nd le arn more, delvi ng into le ss. E spe cially ba sed on rational thi nking on maj or iss ues, applyi ng the ory to guide t he work done is not good e nough, not really understand and grasp t he s pirit and esse nce of the s cie nti fic Outl ook on development, di d not truly a chieve master y, to a ppl y, to a certain extent, affect the In practical w ork, not your head, previous w ork experie nce, l ack of innovati on i nitiatives, study on the chara cteristics of propaganda and ide ologi cal work under the new sit uation through, gri p on grassroots ide ologi cal trends a nd cha nges are not de ep, to promote new initiative s

development and impleme ntation of ideas a nd i nitiatives. Se cond, w ork arrangeme nts, and les s supervisi on. Propaganda and ide ologi cal work i s the obje ctive, w hich nee ds to kee p the conti nuity efforts depl oyed, but stres sed i n the w ork time, less s upervision. For example , color weeke nds in the summer theatrical a ctivities, city square performance s, urgi ng townshi ps, communities and rural area s shows t he impleme ntation i s ina dequate, insufficie nt cult ural an e ducational role to play. T hird base e nough, master gras s-le ss real. Propaga nda a nd i deological work i n the new situati on of char acteristics and regularity of e noug h, deep e nough for grass -roots publi c opini on Dy namics surve y, for grass -root s typically drive les s. For example, r ural cult ure team active, . .. I'm not actively take the i nitiative to take up, the la ck of spirit of daring to, resulti ng in s ome job ha d a lot of power, but no tangible res ults. T hird, i nnovation, lack of motivation. Emancipati on did not e nd, i nnovation doe s not exist. and expl ore ne w methods of ideol ogical a nd cultural w ork is not much, and s ome lack of releva nce a nd timeli ness . 4, di sci pline, l oweri ng, and har d work are la cking. While worki ng and enter prising spirit dow n. No real sol ution to treat your self right, corr ectly treat past honors, their com placency, and w ork to see t heir scores more , less che cking his ow n s hortcomings , like to listen t o the prai se, satisfie d face, online prom otion, there are typi cal, a nd la ck of high sta ndar ds a nd stri ct requireme nts, the effect is real. Second har d drive les s. On har d and

the principl e of simplified E IA of constr uction pr oject s in the regi on. In terms of land, li nked to t he impleme ntation of urba n and rural constr ucti on la nd i ncreas e and de crease, re placement indicat ors for pri ority areas pr oject. Charges , into t he projects of water, ele ctricit y, admini strative charges a nd preferential poli cies. I n the area of taxation, and settle d in areas of industry and its pr oductio n company, withi n 5 years after the compl etion of fiscal incentive s to enter prises . In terms of financi ng, integrati on of la nd, tax, fina ncial a nd other res our ces, a nd construct "G overnme nt credit + busi ne ss credit" credit system, esta blishme nt of marketization, commer cialization and modernizati on of the investment a nd financing platform; effective Bank -enter prise docki ng, e ncourages private capital into the Park, to rais e industry development fund. 5, optimize t he envir onment a nd s ervice i ndus tries. To create "poli cy lowl ands, Hig hlands, i ntegrity of service land, devel opme nt land" as the goal , to optimize the area under devel opme nt environment. All a dministrative law e nforceme nt de partments to a ppoint a full -time pers onnel stationed i n areas dedi cated to coordinating and s olving pr oblems a ssociated wit h busi nesse s in thi s se ctor. When ther e are substantial i ssues, se ctor lea ders arranged to personally interve ne, i n-person, in-person push ta ngibl e area buildi ng a green lig ht, easy line . To furt her reduce a nd sta ndar dize a dministrative examination and approval items, sim plify examination a nd a ppr oval links, im prove efficie ncy; a ccordi ng to the .. . Since the educati onal practi ce of the mass line of the part y, himself s eriously in t he educati on, practical control central "eight rule s" and oppos ing "the four winds" and practi cing "three S uns", a nd che ck the spirit of Jiao Y ulu, i deol ogy, soli cit opini ons base d on out standi ng pr oblems che cked s w ing, careful a nalysi s and reflection. Will now che ck report is as foll ows: first, a dher ence to the party's political dis cipli ne, eig ht in the central provisi on, cha nge the styl e of the ba sic situation of 1, i n com pliance wit h the party' s politi cal di sci pline s. Conscienti ously abi de by the party's politica l disci pline, abi de by t he Constit ution a nd t he rule s and regulati ons of the part y, in the political, i deol ogical and mai ntain highly consistent wit h the CPC Central Committee on t he acti on, t here is no vi olation of the party's politi cal di sci pline problems. 2 , in the im plementati on of the central a uthori ties of the eight provisi ons. Improvi ng resear ch, im proving res earch methods, but there ar e less gras s-roots units, primary first-hand an i nadequate grasp of the problem, w hich is to be strengthene d in the future. Se cond, construction, strictly i n accorda nce with the provi sions to streamli ne and im prove the quality of meetings of the Conference. Thir d, streamlini ng file briefs, cult ure involve s all aspe cts of propaganda and ide olog y, sometimes due to the practical nee ds of inve nt ion notificati ons, this are a nee ds further

(2)非负整数集内排除 0 的集 记作 N*或 N+ Q、Z、R 等其它数集内排除 0 的集,也是这样 表示,例如,整数集内排除 0 的集,表示成 Z* 6.集合的表示方法:集合的表示方法,常用的有列举法和描述法
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(1)列举法:把集合中的元素一一列举出来,写在大括号内。如:{1,2,3,4,5},{x2,3x+2, 5y3-x,x2+y2},…;各元素之间用逗号分开。 (2)描述法:把集合中的所有元素都具有的性质(满足的条件)表示出来,写成 {x | p( x)} 的形式。 (3)韦恩(Venn)图示意 7.两个集合相等:如果两个集合所含的元素完全相同,则称这两个集合相等。

三、数学运用: 1.例题: 例 1.用列举法和描述法表示方程 x 2 ? 2 x ? 3 ? 0 的解集。 答案:列举法: {?1,3} 描述法: {x | x ? x2 ? 2x ? 3, x ? R} 例 2.下列各式中错误的是 (1){奇数}= {x | x ? 2k ? 1, k ? Z} ( )

(2) {x | x ? N *,| x |? 5} ? {1, 2,3, 4} (4) ?3?3 ? N

?x ? y ? 1 (3) {( x, y) | ? } ? {(2, ?1), (?1, 2)} ? xy ? ?2
答案: (4) 例 3.求不等式 2 x ? 3 ? 5 的解集 答案: {x | x ? 4, x ? R}

例 4.求方程 2 x 2 ? x ? 1 ? 0 的所有实数解的集合。 答案: ? 例 5.已知 M ? {2, a, b}, N ? {2a, 2, b2} ,且 M ? N ,求 a , b 的值
1 1 答案: a ? 0, b ? 1 或 a ? , b ? 4 2

例 6.已知集合 A ? ? x ax 2 ? 2 x ? 1 ? 0, x ? R? ,若集合 A 中至多有一个元素,求实数 a 的取值范 围. 【思路分析】本题主要考查元素与集合之间的关系,以及集合的表示法.由描述法可知集合 A 是关于 x 的方程 ax2 ? 2 x ? 1 ? 0 的实数解集,首先考虑方程是不是一元二次方程.
streamlining. Four are standard visits, exce pt as required to participate i n traini ng, no other a ctivity. F ive is to impr ove new s reporti ng, for pr opaga nda w ork strictly accor ding to t he regulati ons . Six is strictly your prese ntation publis hed stri ctly accor ding to the regulations. 罚 济 经 或 决 理 处 好 做 权 作 操 规 违 承 对 。 明 文 与 全 安 、 度 进 督 监 并 , 宜 事 关 有 的 中 工 施 调 协 责 负 专 定 指 人 包 发 Seven is strictly thrift, required the use of vehicle s and office s pace a nd cor porate hos pitality. 3, cha nge the styl e. Propaganda and ide ologi cal work of the new situati on and ne w requirements of the new task s, ha d done a lot of fruitful work, ha s made many achieveme nts, but further cl oser t o the grass r oots, close t o reality, clos e to the mas ses and als o ina dequate innovation must conti nue t o improve. Se cond, t he "four winds" s ome outsta ndi ng iss ues 1 , oppose formalism. One the ory is that he di dn't, wit h less close contact . The oretical st udy of consci ousnes s is not high enough, system performance i s not strong enoug h; more passive lear ning , active lear ning few generalities and learn m ore, delvi ng into le ss. E spe cially ba sed on rational thi nking on major i ssue s, applying t heory to g uide t he work done is not good enoug h, not really understa nd a nd gras p the s pirit and esse nce of the s cientific Outlook on development, did not truly achieve master y, to apply, t o a certai n extent, affect the In practical work, not your hea d, previ ous w ork experie nce, lack of innovation i nitiatives, st udy on the chara cteristics of propaganda and ide ologi cal work under the new sit uation t hr ough, grip on grassroots ideol ogical trends a nd cha nges are not dee p, to pr omote new initiatives development and impleme ntation of ideas a nd i nitiatives. Se cond, w ork arrangements , and less s upervision. Pr opaga nda a nd i deol ogical w ork is the objective, whi ch needs t o keep the continuity efforts depl oyed, but stres sed i n the w ork time, less s upervision. For example , col or weeke nds in the summer theatrical a ctivities, city square performa nce s, urgi ng townshi ps, communitie s and rural areas shows the im plementation is i nade qua te, i ns ufficient cultural a n educational rol e to play. Thir d bas e enough, master grass-le ss real. Propaganda and i de ologi cal work i n the new situati on of char acteristics and regularity of enoug h, de ep e nough for grass -roots publi c opi nion Dynamics s urvey, for grass-r oots typi cally drive le ss. For exampl e, rural culture team a ctive, ... I'm not actively take the i nitiative to take up, the la ck of spirit of daring to, re sulting i n s ome job had a l ot of pow er, but no tangible res ults. T hird, i nnovation, la ck of motivation. Emancipati on di d not end, innovation does not exist. and expl ore ne w methods of ideol ogical a nd cultural w ork is not much, and s ome lack of releva nce a nd timeli ness . 4, di sci pline, l oweri ng, and har d work are la cking. While worki ng and enter prising spirit dow n. No real sol ution to treat your self right, corr ectly treat past honors, their com plac ency, and w ork to see t heir scores more , less che cking his ow n s hortcomings , like to listen t o the prai se, satisfie d face, online prom otion, there are typi cal, a nd la ck of high sta ndar ds a nd stri ct requireme nts, the effect is real. Second har d drive les s. On har d and

2

Since the educati onal practi ce of the mass li ne of the party, himself seri ously i n the e ducation, practi cal control central " eight r ules" and opposing "the four winds" and practi cing "three S uns", and che ck the s pirit of Jiao Yul u, ideol ogy, s olicit opi nions based on outsta ndi ng problems che cked swi ng, careful a nalysi s and refle ction. Will now che ck report i s as follow s: first, adhere nce to t he party's politi cal dis cipline , e ight in the ce ntral provisi on, cha nge the style of the ba sic s ituation of 1, in compliance with t he party's politi cal dis ciplines .

the principl e of simplified E IA of construction pr ojects i n the regi on. In terms of land, linke d to the im plementation of ur ban a nd r ural construction land increase a nd decreas e, repla cement i ndi cators for pri ority areas proje ct. Charges, int o the pr oje cts of water, ele ctricit y, admi nistrative charge s and preferential policies. I n the area of taxation, and settled i n areas of industry and its production company, withi n 5 years after the completion of fiscal i nce ntives to e nterpris es. I n terms of financing, i ntegration of land, tax, fina ncial a nd other res our ces, a nd construct "Governme nt credit + busi nes s credit" cre dit system, establi shment of marketization, commercializ ation a nd m oder nization of the inve stm ent and financing platform; effective Ba nk-enter prise docking, encourage s private ca pital into t he Park, to rais e industry development fund. 5, optimize the environment a nd s ervice i ndustr ies. To create "poli cy low lands, Hig hlands, i ntegrity of service land, dev el opme nt land" as t he goal, t o optimize t he area under devel opment e nvironment. All admi nistrative law enfor cement department s to appoi nt a full-time personne l statione d in area s de dicated t o coordi nating a nd s olving problems ass ociate d with bus ines ses i n this s ector. When t here are substa ntial iss ues, sect or leader s arranged to pers onally i ntervene , in -pers on, i n-pers on pus h tangi ble area buil ding a gree n light, easy li ne. To further re duce and standardiz e admini strative examination a nd a ppr oval items, simplify examination and approval link s, improve effici ency ; according to t he ... Cons cienti ously a bide by the party's political disci pline, abi de by the Constituti on a nd the rules a nd reg ulations of the par ty, i n the political, ide ologi cal and maintai n highly consiste nt with the CPC Ce ntral Committee on the acti on, t here is no viol ation of the party's politi cal dis cipline probl ems. 2, i n the impleme ntation of the central aut horiti es of the eight provisi ons . Improvi ng resear ch, impr oving resear ch methods, but there are le ss grass -root s unit s, primary first-ha nd a n ina dequate grasp of the pr oblem, w hich is to be strengt hene d in the future. Se cond, construction, strictly in a ccorda nce with the provisi ons to streamline and im pr ove the quality of meetings of the Conference. T hird, streamli ning file briefs, culture inv olves all as pect s of propaganda and ide olog y, s ometimes due to the practical nee ds of inve ntion notificati ons, this area nee ds further

1 解:当 a ? 0 时,方程只有一个根 ? ,则 a ? 0 符合题意; 2 当 a ? 0 时,则关于 x 的方程 ax2 ? 2 x ? 1 ? 0 是一元二次方程,由于集合 A 中至多有一个元素,则一 元二次方程 ax2 ? 2 x ? 1 ? 0 有两个相等的实数根或没有实数根,所以△= 4 ? 4a ? 0 ,解得 a ? ?1 . 综上所得,实数 a 的取值范围是 ?a a ? 0或a ? ?1? .
答案: a a ? 0或a ? ?1 2.练习:

?

?

(1)请学生各举一例有限集、无限集、空集。 (2)用列举法表示下列集合: ① {x | x 是 15 的正约数} ③ {( x, y) | x ? y ? 2, x ? 2 y ? 4} ② {( x, y) | x ?{1, 2}, y ?{1, 2}} ④ {x | x ? (?1)n , n ? N}

*⑤ {( x, y) | 3x ? 2 y ? 16, x ? N , y ? N}
8 2 答案:① {1,3,5,15} ② {(1,1),(1, 2),(2,1),(2, 2)} ③ {( , ? )} ④ {?1,1} ⑤ {(2,5),(4, 2)} 3 3

(3)用描述法表示下列集合: ① {1, 4,7,10,13} ; ② {?2, ?4, ?6, ?8, ?10}

答案:① {x | x ? 1 ? 3k , k ? 1, 2,3, 4} ② {x | x ? ?2k , k ? 1, 2,3, 4,5} 四、课堂练习
1. 下列说法正确的是 A. ?1, 2? , ?2,1? 是两个集合 C. ? x ? Q | B. ?(0, 2)? 中有两个元素
2 D. x ? Q | 且x ? x ? 2 ? 0 是空集

(

)

? ?

6 ? ? N ? 是有限集 x ?

?

?

2.将集合 ?x | ?3 ? x ? 3且x ? N? 用列举法表示正确的是 A. ??3, ?2, ?1,0,1, 2,3? C. ?0,1,2,3? B. ??2, ?1,0,1, 2? D. ?1, 2,3?

(

)

3.给出下列4个关系式: 3 ? R,0.3? Q,0 ? N ? ,0 ??0? 其中正确的个数是( A.1个 4.方程组 ? B.2个 C.3个 D.4个

)

?x ? y ? 2 的解集用列举法表示为____________. ?x ? y ? 5
Seven is strictly thrift, required the use of vehicle s and office s pace a nd cor porate hos pitality. 3, cha nge the style. Propaganda and ide ologi cal work of the ne w situati on a nd new requirements of the new task s, ha d done a l ot of fruitful work, ha s made many a chieveme nts, but further clos er to the gras s roots , close t o reality, clos e to the mas ses and als o ina dequate innovation must conti nue to improve. S econd, the "four wi nds" s ome outstandi ng is sues 1, oppose formalism. One theory is t hat he di dn't, with les s cl ose conta ct. The oretical study of consci ousne ss is not hig h enoug h, system performa nce i s not strong enoug h; more passive lear nin g, active lear ning few generalities and lear n more, delvi ng int o less. E spe cially based on rational thi nking on major i ss ues, a pplyi ng theory t o guide the w ork done is not good e nough, not really under stand a nd gras p the spirit and es sence of the scie ntific Outlook on development, did not truly achieve master y, In practical w ork, not y our hea d, previ ous work experience, la ck of innovation initiatives, study on the characteristi cs of pr opaga nda a nd ideol ogical work under the ne w situati on thr oug h, grip on

streamlining. Four are standard vi sits, exce pt as required to participate in traini ng, no other activity. Five is to impr ove new s reporting, for pr opaga nda w ork strictly a ccor ding to t he regulati ons. Six is strictly your pres entation publis he d strictly accor ding to t he regulati ons . 罚 济 经 或 决 理 处 好 做 权 作 操 规 违 承 对 。 明 文 与 全 安 、 度 进 督 监 并 , 宜 事 关 有 的 中 工 施 调 协 责 负 专 定 指 人 包 发

to appl y, to a certain extent, affect the development a nd impleme ntation of ideas a nd i nitiatives. Se cond, w ork arrangeme nts, and less supervisi on. Propaganda and i de ological work is t he objective , whi ch needs to keep t he continuity efforts de ployed, but stre ssed i n the w ork time, less supervisi on. For example, color w eekends i n the s ummer theatrical a ctivities, city square performa nce s, urging towns hips, communitie s and rural areas s how s the impl ement ation is ina de quate, i nsufficie nt cultural an e ducational role t o play. Third base e nough, master gras s-le ss real. Propaga nda a nd i deol ogical work in t he ne w situati on of characteri stics a nd reg ularity of enoug h, de ep e noug h for grass -root s public opi nion Dynami cs s urvey, for gras s-roots typi cally drive le ss. For example , rural culture team active , ... I'm not actively take the i nitiative to take up, the la ck of spirit of daring to, res ulting in some j ob had a lot of powe r, but no ta ngibl e results . Third, innovation, lack of motivation. Ema nci pation did not e nd, i nnovation doe s not exist. grassroots i deol ogica l trends and changes are not deep, t o promote new i nitiatives and expl ore new met hods of ide ologi cal and cultural w ork is not much, and some la ck of relevance and timeline ss. 4 , dis cipli ne, l owering , and hard w ork are lacki ng. While working a nd e nterpri sing s pirit down. No real soluti on to treat yourself right, correctly treat pa st honor s, their compla cency, and work to s ee their s core s more, les s checki ng his own shortcomi ngs, like to liste n to the praise, satisfied face, onli ne pr omotion, ther e are typical , and lack of hig h standards and strict requirements , the effect is r eal. Second hard drive less . On hard a nd

the principl e of simplified E IA of constr uction pr oject s in the regi on. In terms of land, li nked to t he impleme ntation of urba n and rural constr ucti on la nd i ncreas e and de crease, re placement indicat ors for pri ority areas pr oject. Charges , into t he projects of water, ele ctricit y, admini strative charges a nd preferential poli cies. I n the area of taxation, and settle d in areas of industry and its pr oductio n company, withi n 5 years after the compl etion of fiscal incentive s to enter prises . In terms of financi ng, integrati on of la nd, tax, fina ncial a nd other res our ces, a nd construct "G overnme nt credit + busi ne ss credit" credit system, esta blishme nt of marketization, commer cialization and modernizati on of the investment a nd financing platform; effective Bank -enter prise docki ng, e ncourages private capital into the Park, to rais e industry development fund. 5, optimize t he envir onment a nd s ervice i ndus tries. To create "poli cy lowl ands, Hig hlands, i ntegrity of service land, devel opme nt land" as the goal , to optimize the area under devel opme nt environment. All a dministrative law e nforceme nt de partments to a ppoint a full -time pers onnel stationed i n areas dedi cated to coordinating and s olving pr oblems a ssociated wit h busi nesse s in thi s se ctor. When ther e are substantial i ssues, se ctor lea ders arranged to personally interve ne, i n-person, in-person push ta ngibl e area buildi ng a green lig ht, easy line . To furt her reduce a nd sta ndar dize a dministrative examination and approval items, sim plify examination a nd a ppr oval links, im prove efficie ncy; a ccordi ng to the .. . Since the educati onal practi ce of the mass line of the part y, himself s eriously in t he educati on, practical control central "eight rule s" and oppos ing "the four winds" and practi cing "three S uns", a nd che ck the spirit of Jiao Y ulu, i deol ogy, soli cit opini ons base d on out standi ng pr oblems che cked s w ing, careful a nalysi s and reflection. Will now che ck report is as foll ows: first, a dher ence to the party's political dis cipli ne, eig ht in the central provisi on, cha nge the styl e of the ba sic situation of 1, i n com pliance wit h the party' s politi cal di sci pline s. Conscienti ously abi de by the party's politica l disci pline, abi de by t he Constit ution a nd t he rule s and regulati ons of the part y, in the political, i deol ogical and mai ntain highly consistent wit h the CPC Central Committee on t he acti on, t here is no vi olation of the party's politi cal di sci pline problems. 2 , in the im plementati on of the central a uthori ties of the eight provisi ons. Improvi ng resear ch, im proving res earch methods, but there ar e less gras s-roots units, primary first-hand an i nadequate grasp of the problem, w hich is to be strengthene d in the future. Se cond, construction, strictly i n accorda nce with the provi sions to streamli ne and im prove the quality of meetings of the Conference. Thir d, streamlini ng file briefs, cult ure involve s all aspe cts of propaganda and ide olog y, sometimes due to the practical nee ds of inve nt ion notificati ons, this are a nee ds further

2 5.已知集合A= 0,1, x ? x 则 x 在实数范围内不能取哪些值___________.

?

?

6 .( 创 新 题 ) 已 知 集 合 S ? ?a, b, c? 中 的 三 个 元 素 是 ?ABC 的 三 边 长 , 那 么 ?ABC 一 定 不 是 ( ) A.锐角三角形 B.直角三角形 C.钝角三角形 D.等腰三角形

五、回顾小结: 1.集合的有关概念 2.集合的表示方法 3.常用数集的记法 六、课外作业: 一、选择题 1.下列元素与集合的关系中正确的是(
1 A. ? N 2

) C.|-3|?N* D.-3.2?Q

B.2?{x?R|x≥ 3 }

2.给出下列四个命题: (1)很小的实数可以构成集合; (2)集合{y|y=x2-1}与集合{(x,y)|y=x2-1}是同一个集合; (3)1,
3 6 1 , , ? ,0.5 这些数字组成的集合有 5 个元素; 2 4 2

(4)集合{(x,y)|xy≤0,x,y?R}是指第二象限或第四象限内的点的集合. 以上命题中,正确命题的个数是( A.0 B.1 C.2 D.3 ) )

3.下列集合中表示同一集合的是( A.M={(3,2)},N={(2,3)} B.M={3,2},N={(2,3)} C.M={(x,y)|x+y=1},N={y|x+y=1} D.M={1,2},N={2,1}

4.已知 x?N,则方程 x2 ? x ? 2 ? 0 的解集为( A.{x|x=-2} B. {x|x=1 或 x=-2}

) C. {x|x=1} D.? ) D.9
In practical work, not your hea d, previ ous w ork experie nce, lack of innovation i nitiatives, st udy on the chara cteristics of propaganda and ide ologi cal work under the new sit uation t hr ough, grip on grassroots ideol ogical trends a nd cha nges are not dee p, to pr omote new initiatives

5.已知集合 M={m?N|8-m?N},则集合 M 中元素个数是( A.6 B.7
Seven is strictly thrift, required the use of vehicle s and office s pace a nd cor porate hos pitality. 3, cha nge the styl e.

C.8
4

streamlining. Four are standard visits, exce pt as required to participate i n traini ng, no other a ctivity. F ive is to impr ove new s reporti ng, for pr opaga nda w ork strictly accor ding to t he regulati ons . Six is strictly your prese ntation publis hed stri ctly accor ding to the regulations. 罚 济 经 或 决 理 处 好 做 权 作 操 规 违 承 对 。 明 文 与 全 安 、 度 进 督 监 并 , 宜 事 关 有 的 中 工 施 调 协 责 负 专 定 指 人 包 发

Propaganda and ide ologi cal work of the new situati on and ne w requirements of the new task s, ha d done a lot of fruitful work, ha s made many achieveme nts, but further cl oser t o the grass r oots, close t o reality, clos e to the mas ses and als o ina dequate innovation must conti nue t o improve. Se cond, t he "four winds" s ome outsta ndi ng iss ues 1 , oppose formalism. One the ory is that he di dn't, wit h less close contact . The oretical st udy of consci ousnes s is not high enough, system performance i s not strong enoug h; more passive lear ning , active lear ning few generalities and learn m ore, delvi ng into le ss. E spe cially ba sed on rational thi nking on major i ssue s, applying t heory to g uide t he work done is not good enoug h, not really understa nd a nd gras p the s pirit and esse nce of the s cientific Outlook on development, did not truly achieve master y, to apply, t o a certai n extent, affect the

development and impleme ntation of ideas a nd i nitiatives. Se cond, w ork arrangements , and less s upervision. Pr opaga nda a nd i deol ogical w ork is the objective, whi ch needs t o keep the continuity efforts depl oyed, but stres sed i n the w ork time, less s upervision. For example , col or weeke nds in the summer theatrical a ctivities, city square performa nce s, urgi ng townshi ps, communitie s and rural areas shows the im plementation is i nade qua te, i ns ufficient cultural a n educational rol e to play. Thir d bas e enough, master grass-le ss real. Propaganda and i de ologi cal work i n the new situati on of char acteristics and regularity of enoug h, de ep e nough for grass -roots publi c opi nion Dynamics s urvey, for grass-r oots typi cally drive le ss. For exampl e, rural culture team a ctive, ... I'm not actively take the i nitiative to take up, the la ck of spirit of daring to, re sulting i n s ome job had a l ot of pow er, but no tangible res ults. T hird, i nnovation, la ck of motivation. Emancipati on di d not end, innovation does not exist.

and expl ore ne w methods of ideol ogical a nd cultural w ork is not much, and s ome lack of releva nce a nd timeli ness . 4, di sci pline, l oweri ng, and har d work are la cking. While worki ng and enter prising spirit dow n. No real sol ution to treat your self right, corr ectly treat past honors, their com plac ency, and w ork to see t heir scores more , less che cking his ow n s hortcomings , like to listen t o the prai se, satisfie d face, online prom otion, there are typi cal, a nd la ck of high sta ndar ds a nd stri ct requireme nts, the effect is real. Second har d drive les s. On har d and

Since the educati onal practi ce of the mass li ne of the party, himself seri ously i n the e ducation, practi cal control central " eight r ules" and opposing "the four winds" and practi cing "three S uns", and che ck the s pirit of Jiao Yul u, ideol ogy, s olicit opi nions based on outsta ndi ng problems che cked swi ng, careful a nalysi s and refle ction. Will now che ck report i s as follow s: first, adhere nce to t he party's politi cal dis cipline , e ight in the ce ntral provisi on, cha nge the style of the ba sic s ituation of 1, in compliance with t he party's politi cal dis ciplines .

the principl e of simplified E IA of construction pr ojects i n the regi on. In terms of land, linke d to the im plementation of ur ban a nd r ural construction land increase a nd decreas e, repla cement i ndi cators for pri ority areas proje ct. Charges, int o the pr oje cts of water, ele ctricit y, admi nistrative charge s and preferential policies. I n the area of taxation, and settled i n areas of industry and its production company, withi n 5 years after the completion of fiscal i nce ntives to e nterpris es. I n terms of financing, i ntegration of land, tax, fina ncial a nd other res our ces, a nd construct "Governme nt credit + busi nes s credit" cre dit system, establi shment of marketization, commercializ ation a nd m oder nization of the inve stm ent and financing platform; effective Ba nk-enter prise docking, encourage s private ca pital into t he Park, to rais e industry development fund. 5, optimize the environment a nd s ervice i ndustr ies. To create "poli cy low lands, Hig hlands, i ntegrity of service land, dev el opme nt land" as t he goal, t o optimize t he area under devel opment e nvironment. All admi nistrative law enfor cement department s to appoi nt a full-time personne l statione d in area s de dicated t o coordi nating a nd s olving problems ass ociate d with bus ines ses i n this s ector. When t here are substa ntial iss ues, sect or leader s arranged to pers onally i ntervene , in -pers on, i n-pers on pus h tangi ble area buil ding a gree n light, easy li ne. To further re duce and standardiz e admini strative examination a nd a ppr oval items, simplify examination and approval link s, improve effici ency ; according to t he ... Cons cienti ously a bide by the party's political disci pline, abi de by the Constituti on a nd the rules a nd reg ulations of the par ty, i n the political, ide ologi cal and maintai n highly consiste nt with the CPC Ce ntral Committee on the acti on, t here is no viol ation of the party's politi cal dis cipline probl ems. 2, i n the impleme ntation of the central aut horiti es of the eight provisi ons . Improvi ng resear ch, impr oving resear ch methods, but there are le ss grass -root s unit s, primary first-ha nd a n ina dequate grasp of the pr oblem, w hich is to be strengt hene d in the future. Se cond, construction, strictly in a ccorda nce with the provisi ons to streamline and im pr ove the quality of meetings of the Conference. T hird, streamli ning file briefs, culture inv olves all as pect s of propaganda and ide olog y, s ometimes due to the practical nee ds of inve ntion notificati ons, this area nee ds further

二、填空题 6.用符号“?”或“?”填空: 0_______N, 5 ______N, 16 ______N. 7.用列举法表示 A={y|y=x2+1,-2≤x≤2,x?Z}为_______________. 8.用描述法表示集合“方程 x2-2x+3=0 的解集”为_____________. 9.集合{x|x>3}与集合{t|t>3}是否表示同一集合?________ 10.已知集合 P={x|2<x<a,x?N},已知集合 P 中恰有 3 个元素,则整数 a=_________. 三、解答题 11.已知集合 A={0,1,2},集合 B={x|x=ab,a?A,b?A}. (1)用列举法写出集合 B; (2)判断集合 B 的元素和集合 A 的关系.

12.已知集合{1,a,b}与{-1,-b,1}是同一集合,求实数 a、b 的值.

13.(探究题)下面三个集合:① ? x | y ? x 2 ? 2? ,② ? y | y ? x 2 ? 2? ,③ ?( x, y ) | y ? x 2 ? 2? (1)它们是不是相同的集合? (2)试用文字语言叙述各集合的含义.

第一章集合与函数的概念 1.1.1 集合的含义与表示 【课堂练习】 1.D 2. C 3.B 4. ?? , ? ? ?

?? 7 ?? 2

3 ?? 2 ??

5. x ? 0,1,

1? 5 2

6.D

【课后作业】 选择题 1-5 BADCC

streamlining. Four are standard vi sits, exce pt as required to participate in traini ng, no other activity. Five is to impr ove new s reporting, for pr opaga nda w ork strictly a ccor ding to t he regulati ons. Six is strictly your pres entation publis he d strictly accor ding to t he regulati ons . 罚 济 经 或 决 理 处 好 做 权 作 操 规 违 承 对 。 明 文 与 全 安 、 度 进 督 监 并 , 宜 事 关 有 的 中 工 施 调 协 责 负 专 定 指 人 包 发

Seven is strictly thrift, required the use of vehicle s and office s pace a nd cor porate hos pitality. 3, cha nge the style.

Propaganda and ide ologi cal work of the ne w situati on a nd new requirements of the new task s, ha d done a l ot of fruitful work, ha s made many a chieveme nts, but further clos er to the gras s roots , close t o reality, clos e to the mas ses and als o ina dequate innovation must conti nue to improve. S econd, the "four wi nds" s ome outstandi ng is sues 1, oppose formalism. One theory is t hat he di dn't, with les s cl ose conta ct. The oretical study of consci ousne ss is not hig h enoug h, system performa nce i s not strong enoug h; more passive lear nin g, active lear ning few generalities and lear n more, delvi ng int o less. E spe cially based on rational thi nking on major i ss ues, a pplyi ng theory t o guide the w ork done is not good e nough, not really under stand a nd gras p the spirit and es sence of the scie ntific Outlook on development, did not truly achieve master y, In practical w ork, not y our hea d, previ ous work experience, la ck of innovation initiatives, study on the characteristi cs of pr opaga nda a nd ideol ogical work under the ne w situati on thr oug h, grip on

to appl y, to a certain extent, affect the development a nd impleme ntation of ideas a nd i nitiatives. Se cond, w ork arrangeme nts, and less supervisi on. Propaganda and i de ological work is t he objective , whi ch needs to keep t he continuity efforts de ployed, but stre ssed i n the w ork time, less supervisi on. For example, color w eekends i n the s ummer theatrical a ctivities, city square performa nce s, urging towns hips, communitie s and rural areas s how s the impl ement ation is ina de quate, i nsufficie nt cultural an e ducational role t o play. Third base e nough, master gras s-le ss real. Propaga nda a nd i deol ogical work in t he ne w situati on of characteri stics a nd reg ularity of enoug h, de ep e noug h for grass -root s public opi nion Dynami cs s urvey, for gras s-roots typi cally drive le ss. For example , rural culture team active , ... I'm not actively take the i nitiative to take up, the la ck of spirit of daring to, res ulting in some j ob had a lot of powe r, but no ta ngibl e results . Third, innovation, lack of motivation. Ema nci pation did not e nd, i nnovation doe s not exist. grassroots i deol ogica l trends and changes are not deep, t o promote new i nitiatives and expl ore new met hods of ide ologi cal and cultural w ork is not much, and some la ck of relevance and timeline ss. 4 , dis cipli ne, l owering , and hard w ork are lacki ng. While working a nd e nterpri sing s pirit down. No real soluti on to treat yourself right, correctly treat pa st honor s, their compla cency, and work to s ee their s core s more, les s checki ng his own shortcomi ngs, like to liste n to the praise, satisfied face, onli ne pr omotion, ther e are typical , and lack of hig h standards and strict requirements , the effect is r eal. Second hard drive less . On hard a nd

the principl e of simplified E IA of constr uction pr oject s in the regi on. In terms of land, li nked to t he impleme ntation of urba n and rural constr ucti on la nd i ncreas e and de crease, re placement indicat ors for pri ority areas pr oject. Charges , into t he projects of water, ele ctricit y, admini strative charges a nd preferential poli cies. I n the area of taxation, and settle d in areas of industry and its pr oductio n company, withi n 5 years after the compl etion of fiscal incentive s to enter prises . In terms of financi ng, integrati on of la nd, tax, fina ncial a nd other res our ces, a nd construct "G overnme nt credit + busi ne ss credit" credit system, esta blishme nt of marketization, commer cialization and modernizati on of the investment a nd financing platform; effective Bank -enter prise docki ng, e ncourages private capital into the Park, to rais e industry development fund. 5, optimize t he envir onment a nd s ervice i ndus tries. To create "poli cy lowl ands, Hig hlands, i ntegrity of service land, devel opme nt land" as the goal , to optimize the area under devel opme nt environment. All a dministrative law e nforceme nt de partments to a ppoint a full -time pers onnel stationed i n areas dedi cated to coordinating and s olving pr oblems a ssociated wit h busi nesse s in thi s se ctor. When ther e are substantial i ssues, se ctor lea ders arranged to personally interve ne, i n-person, in-person push ta ngibl e area buildi ng a green lig ht, easy line . To furt her reduce a nd sta ndar dize a dministrative examination and approval items, sim plify examination a nd a ppr oval links, im prove efficie ncy; a ccordi ng to the .. . Since the educati onal practi ce of the mass line of the part y, himself s eriously in t he educati on, practical control central "eight rule s" and oppos ing "the four winds" and practi cing "three S uns", a nd che ck the spirit of Jiao Y ulu, i deol ogy, soli cit opini ons base d on out standi ng pr oblems che cked s w ing, careful a nalysi s and reflection. Will now che ck report is as foll ows: first, a dher ence to the party's political dis cipli ne, eig ht in the central provisi on, cha nge the styl e of the ba sic situation of 1, i n com pliance wit h the party' s politi cal di sci pline s. Conscienti ously abi de by the party's politica l disci pline, abi de by t he Constit ution a nd t he rule s and regulati ons of the part y, in the political, i deol ogical and mai ntain highly consistent wit h the CPC Central Committee on t he acti on, t here is no vi olation of the party's politi cal di sci pline problems. 2 , in the im plementati on of the central a uthori ties of the eight provisi ons. Improvi ng resear ch, im proving res earch methods, but there ar e less gras s-roots units, primary first-hand an i nadequate grasp of the problem, w hich is to be strengthene d in the future. Se cond, construction, strictly i n accorda nce with the provi sions to streamli ne and im prove the quality of meetings of the Conference. Thir d, streamlini ng file briefs, cult ure involve s all aspe cts of propaganda and ide olog y, sometimes due to the practical nee ds of inve nt ion notificati ons, this are a nee ds further

填空题 6. ? ? ? 解答题

7.

?2,4,5?

8.

?x | x

2

? 2 x ? 3 ? 0?

9.是 10. 6

11. B ? {0,1,2,4} 集合 A 中的元素都在集合 B 中。 12.(1)若 a ? ?1, b ? ?b ? 0 (2)若 a ? ?b, b ? ?1则a ? 1(不合题意,舍去) 13.(1)不是 (2)集合①是指自变量 x 的取值范围,是全体实数; 集合②是指函数值 y 的取值范围,与集合 ? y | y ? ?2? 相等 集合③是抛物线 y ? x2 ? 2 上的点所构成的集合。 综上 a ? ?1, b ? 0

streamlining. Four are standard visits, exce pt as required to participate i n traini ng, no other a ctivity. F ive is to impr ove new s reporti ng, for pr opaga nda w ork strictly accor ding to t he regulati ons . Six is strictly your prese ntation publis hed stri ctly accor ding to the regulations. 罚 济 经 或 决 理 处 好 做 权 作 操 规 违 承 对 。 明 文 与 全 安 、 度 进 督 监 并 , 宜 事 关 有 的 中 工 施 调 协 责 负 专 定 指 人 包 发

Seven is strictly thrift, required the use of vehicle s and office s pace a nd cor porate hos pitality. 3, cha nge the styl e.

Propaganda and ide ologi cal work of the new situati on and ne w requirements of the new task s, ha d done a lot of fruitful work, ha s made many achieveme nts, but further cl oser t o the grass r oots, close t o reality, clos e to the mas ses and als o ina dequate innovation must conti nue t o improve. Se cond, t he "four winds" s ome outsta ndi ng iss ues 1 , oppose formalism. One the ory is that he di dn't, wit h less close contact . The oretical st udy of consci ousnes s is not high enough, system performance i s not strong enoug h; more passive lear ning , active lear ning few generalities and learn m ore, delvi ng into le ss. E spe cially ba sed on rational thi nking on major i ssue s, applying t heory to g uide t he work done is not good enoug h, not really understa nd a nd gras p the s pirit and esse nce of the s cientific Outlook on development, did not truly achieve master y, to apply, t o a certai n extent, affect the In practical work, not your hea d, previ ous w ork experie nce, lack of innovation i nitiatives, st udy on the chara cteristics of propaganda and ide ologi cal work under the new sit uation t hr ough, grip on grassroots ideol ogical trends a nd cha nges are not dee p, to pr omote new initiatives

development and impleme ntation of ideas a nd i nitiatives. Se cond, w ork arrangements , and less s upervision. Pr opaga nda a nd i deol ogical w ork is the objective, whi ch needs t o keep the continuity efforts depl oyed, but stres sed i n the w ork time, less s upervision. For example , col or weeke nds in the summer theatrical a ctivities, city square performa nce s, urgi ng townshi ps, communitie s and rural areas shows the im plementation is i nade qua te, i ns ufficient cultural a n educational rol e to play. Thir d bas e enough, master grass-le ss real. Propaganda and i de ologi cal work i n the new situati on of char acteristics and regularity of enoug h, de ep e nough for grass -roots publi c opi nion Dynamics s urvey, for grass-r oots typi cally drive le ss. For exampl e, rural culture team a ctive, ... I'm not actively take the i nitiative to take up, the la ck of spirit of daring to, re sulting i n s ome job had a l ot of pow er, but no tangible res ults. T hird, i nnovation, la ck of motivation. Emancipati on di d not end, innovation does not exist.

and expl ore ne w methods of ideol ogical a nd cultural w ork is not much, and s ome lack of releva nce a nd timeli ness . 4, di sci pline, l oweri ng, and har d work are la cking. While worki ng and enter prising spirit dow n. No real sol ution to treat your self right, corr ectly treat past honors, their com plac ency, and w ork to see t heir scores more , less che cking his ow n s hortcomings , like to listen t o the prai se, satisfie d face, online prom otion, there are typi cal, a nd la ck of high sta ndar ds a nd stri ct requireme nts, the effect is real. Second har d drive les s. On har d and

6

Since the educati onal practi ce of the mass li ne of the party, himself seri ously i n the e ducation, practi cal control central " eight r ules" and opposing "the four winds" and practi cing "three S uns", and che ck the s pirit of Jiao Yul u, ideol ogy, s olicit opi nions based on outsta ndi ng problems che cked swi ng, careful a nalysi s and refle ction. Will now che ck report i s as follow s: first, adhere nce to t he party's politi cal dis cipline , e ight in the ce ntral provisi on, cha nge the style of the ba sic s ituation of 1, in compliance with t he party's politi cal dis ciplines .

the principl e of simplified E IA of construction pr ojects i n the regi on. In terms of land, linke d to the im plementation of ur ban a nd r ural construction land increase a nd decreas e, repla cement i ndi cators for pri ority areas proje ct. Charges, int o the pr oje cts of water, ele ctricit y, admi nistrative charge s and preferential policies. I n the area of taxation, and settled i n areas of industry and its production company, withi n 5 years after the completion of fiscal i nce ntives to e nterpris es. I n terms of financing, i ntegration of land, tax, fina ncial a nd other res our ces, a nd construct "Governme nt credit + busi nes s credit" cre dit system, establi shment of marketization, commercializ ation a nd m oder nization of the inve stm ent and financing platform; effective Ba nk-enter prise docking, encourage s private ca pital into t he Park, to rais e industry development fund. 5, optimize the environment a nd s ervice i ndustr ies. To create "poli cy low lands, Hig hlands, i ntegrity of service land, dev el opme nt land" as t he goal, t o optimize t he area under devel opment e nvironment. All admi nistrative law enfor cement department s to appoi nt a full-time personne l statione d in area s de dicated t o coordi nating a nd s olving problems ass ociate d with bus ines ses i n this s ector. When t here are substa ntial iss ues, sect or leader s arranged to pers onally i ntervene , in -pers on, i n-pers on pus h tangi ble area buil ding a gree n light, easy li ne. To further re duce and standardiz e admini strative examination a nd a ppr oval items, simplify examination and approval link s, improve effici ency ; according to t he ... Cons cienti ously a bide by the party's political disci pline, abi de by the Constituti on a nd the rules a nd reg ulations of the par ty, i n the political, ide ologi cal and maintai n highly consiste nt with the CPC Ce ntral Committee on the acti on, t here is no viol ation of the party's politi cal dis cipline probl ems. 2, i n the impleme ntation of the central aut horiti es of the eight provisi ons . Improvi ng resear ch, impr oving resear ch methods, but there are le ss grass -root s unit s, primary first-ha nd a n ina dequate grasp of the pr oblem, w hich is to be strengt hene d in the future. Se cond, construction, strictly in a ccorda nce with the provisi ons to streamline and im pr ove the quality of meetings of the Conference. T hird, streamli ning file briefs, culture inv olves all as pect s of propaganda and ide olog y, s ometimes due to the practical nee ds of inve ntion notificati ons, this area nee ds further

§1.1.1 集合的含义与表示
一. 教学目标: l.知识与技能 (1)通过实例,了解集合的含义,体会元素与集合的属于关系; (2)知道常用数集及其专用记号; (3)了解集合中元素的确定性.互异性.无序性; (4)会用集合语言表示有关数学对象; (5)培养学生抽象概括的能力. 2. 过程与方法 (1)让学生经历从集合实例中抽象概括出集合共同特征的过程,感知集合的含义. (2)让学生归纳整理本节所学知识. 3. 情感.态度与价值观 使学生感受到学习集合的必要性,增强学习的积极性. 二. 教学重点.难点 重点:集合的含义与表示方法. 难点:表示法的恰当选择. 三. 学法与教学用具 1. 学法:学生通过阅读教材,自主学习.思考.交流.讨论和概括,从而更好地完成本节课的教学目标. 2. 教学用具:投影仪. 四. 教学思路 (一)创设情景,揭示课题 1.教师首先提出问题:在初中,我们已经接触过一些集合,你能举出一些集合的例子吗? 引导学生回忆.举例和互相交流. 与此同时,教师对学生的活动给予评价. 2.接着教师指出:那么,集合的含义是什么呢?这就是我们这一堂课所要学习的内容. (二)研探新知 1.教师利用多媒体设备向学生投影出下面 9 个实例: (1)1—20 以内的所有质数; (2)我国古代的四大发明; (3)所有的安理会常任理事国; (4)所有的正方形; (5)海南省在 2004 年 9 月之前建成的所有立交桥; (6)到一个角的两边距离相等的所有的点; (7)方程 x ? 5x ? 6 ? 0 的所有实数根;
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(8)不等式 x ? 3 ? 0 的所有解; (9)国兴中学 2004 年 9 月入学的高一学生的全体. 2.教师组织学生分组讨论:这 9 个实例的共同特征是什么? 3.每个小组选出——位同学发表本组的讨论结果,在此基础上,师生共同概括出 9 个实例的特征,并给出集合的 含义. 一般地,指定的某些对象的全体称为集合(简称为集).集合中的每个对象叫作这个集合的元素. 4.教师指出:集合常用大写字母 A,B,C,D,…表示,元素常用小写字母 a, b, c, d …表示. (三)质疑答辩,排难解惑,发展思维 1.教师引导学生阅读教材中的相关内容,思考:集合中元素有什么特点?并注意个别辅导,解答学生疑难.使学 生明确集合元素的三大特性, 即:确定性.互异性和无序性.只要构成两个集合的元素是一样的,我们就称这两个集合相
streamlining. Four are standard vi sits, exce pt as required to participate in traini ng, no other activity. Five is to impr ove new s reporting, for pr opaga nda w ork strictly a ccor ding to t he regulati ons. Six is strictly your pres entation publis he d strictly accor ding to t he regulati ons . 罚 济 经 或 决 理 处 好 做 权 作 操 规 违 承 对 。 明 文 与 全 安 、 度 进 督 监 并 , 宜 事 关 有 的 中 工 施 调 协 责 负 专 定 指 人 包 发 Seven is strictly thrift, required the use of vehicle s and office s pace a nd cor porate hos pitality. 3, cha nge the style. Propaganda and ide ologi cal work of the ne w situati on a nd new requirements of the new task s, ha d done a l ot of fruitful work, ha s made many a chieveme nts, but further clos er to the gras s roots , close t o reality, clos e to the mas ses and als o ina dequate innovation must conti nue to improve. S econd, the "four wi nds" s ome outstandi ng is sues 1, oppose formalism. One theory is t hat he di dn't, with les s cl ose conta ct. The oretical study of consci ousne ss is not hig h enoug h, system performa nce i s not strong enoug h; more passive lear nin g, active lear ning few generalities and lear n more, delvi ng int o less. E spe cially based on rational thi nking on major i ss ues, a pplyi ng theory t o guide the w ork done is not good e nough, not really under stand a nd gras p the spirit and es sence of the scie ntific Outlook on development, did not truly achieve master y, In practical w ork, not y our hea d, previ ous work experience, la ck of innovation initiatives, study on the characteristi cs of pr opaga nda a nd ideol ogical work under the ne w situati on thr oug h, grip on to appl y, to a certain extent, affect the development a nd impleme ntation of ideas a nd i nitiatives. Se cond, w ork arrangeme nts, and less supervisi on. Propaganda and i de ological work is t he objective , whi ch needs to keep t he continuity efforts de ployed, but stre ssed i n the w ork time, less supervisi on. For example, color w eekends i n the s ummer theatrical a ctivities, city square performa nce s, urging towns hips, communitie s and rural areas s how s the impl ement ation is ina de quate, i nsufficie nt cultural an e ducational role t o play. Third base e nough, master gras s-le ss real. Propaga nda a nd i deol ogical work in t he ne w situati on of characteri stics a nd reg ularity of enoug h, de ep e noug h for grass -root s public opi nion Dynami cs s urvey, for gras s-roots typi cally drive le ss. For example , rural culture team active , ... I'm not actively take the i nitiative to take up, the la ck of spirit of daring to, res ulting in some j ob had a lot of powe r, but no ta ngibl e results . Third, innovation, lack of motivation. Ema nci pation did not e nd, i nnovation doe s not exist. grassroots i deol ogica l trends and changes are not deep, t o promote new i nitiatives and expl ore new met hods of ide ologi cal and cultural w ork is not much, and some la ck of relevance and timeline ss. 4 , dis cipli ne, l owering , and hard w ork are lacki ng. While working a nd e nterpri sing s pirit down. No real soluti on to treat yourself right, correctly treat pa st honor s, their compla cency, and work to s ee their s core s more, les s checki ng his own shortcomi ngs, like to liste n to the praise, satisfied face, onli ne pr omotion, ther e are typical , and lack of hig h standards and strict requirements , the effect is r eal. Second hard drive less . On hard a nd

the principl e of simplified E IA of constr uction pr oject s in the regi on. In terms of land, li nked to t he impleme ntation of urba n and rural constr ucti on la nd i ncreas e and de crease, re placement indicat ors for pri ority areas pr oject. Charges , into t he projects of water, ele ctricit y, admini strative charges a nd preferential poli cies. I n the area of taxation, and settle d in areas of industry and its pr oductio n company, withi n 5 years after the compl etion of fiscal incentive s to enter prises . In terms of financi ng, integrati on of la nd, tax, fina ncial a nd other res our ces, a nd construct "G overnme nt credit + busi ne ss credit" credit system, esta blishme nt of marketization, commer cialization and modernizati on of the investment a nd financing platform; effective Bank -enter prise docki ng, e ncourages private capital into the Park, to rais e industry development fund. 5, optimize t he envir onment a nd s ervice i ndus tries. To create "poli cy lowl ands, Hig hlands, i ntegrity of service land, devel opme nt land" as the goal , to optimize the area under devel opme nt environment. All a dministrative law e nforceme nt de partments to a ppoint a full -time pers onnel stationed i n areas dedi cated to coordinating and s olving pr oblems a ssociated wit h busi nesse s in thi s se ctor. When ther e are substantial i ssues, se ctor lea ders arranged to personally interve ne, i n-person, in-person push ta ngibl e area buildi ng a green lig ht, easy line . To furt her reduce a nd sta ndar dize a dministrative examination and approval items, sim plify examination a nd a ppr oval links, im prove efficie ncy; a ccordi ng to the .. . Since the educati onal practi ce of the mass line of the part y, himself s eriously in t he educati on, practical control central "eight rule s" and oppos ing "the four winds" and practi cing "three S uns", a nd che ck the spirit of Jiao Y ulu, i deol ogy, soli cit opini ons base d on out standi ng pr oblems che cked s w ing, careful a nalysi s and reflection. Will now che ck report is as foll ows: first, a dher ence to the party's political dis cipli ne, eig ht in the central provisi on, cha nge the styl e of the ba sic situation of 1, i n com pliance wit h the party' s politi cal di sci pline s. Conscienti ously abi de by the party's politica l disci pline, abi de by t he Constit ution a nd t he rule s and regulati ons of the part y, in the political, i deol ogical and mai ntain highly consistent wit h the CPC Central Committee on t he acti on, t here is no vi olation of the party's politi cal di sci pline problems. 2 , in the im plementati on of the central a uthori ties of the eight provisi ons. Improvi ng resear ch, im proving res earch methods, but there ar e less gras s-roots units, primary first-hand an i nadequate grasp of the problem, w hich is to be strengthene d in the future. Se cond, construction, strictly i n accorda nce with the provi sions to streamli ne and im prove the quality of meetings of the Conference. Thir d, streamlini ng file briefs, cult ure involve s all aspe cts of propaganda and ide olog y, sometimes due to the practical nee ds of inve nt ion notificati ons, this are a nee ds further

等. 2.教师组织引导学生思考以下问题: 判断以下元素的全体是否组成集合,并说明理由: (1)大于 3 小于 11 的偶数; (2)我国的小河流. 让学生充分发表自己的建解. 3. 让学生自己举出一些能够构成集合的例子以及不能构成集合的例子, 并说明理由.教师对学生的学习活动给予 及时的评价. 4.教师提出问题,让学生思考 (1)如果用 A 表示高—(3)班全体学生组成的集合,用 a 表示高一(3)班的一位同学, b 是高一(4)班的一位同学, 那么 a , b 与集合 A 分别有什么关系?由此引导学生得出元素与集合的关系有两种:属于和不属于. 如果 a 是集合 A 的元素,就说 a 属于集合 A,记作 a ? A . 如果 a 不是集合 A 的元素,就说 a 不属于集合 A,记作 a ? A . (2)如果用 A 表示“所有的安理会常任理事国”组成的集合,则中国.日本与集合 A 的关系分别是什么?请用数学 符号分别表示. (3)让学生完成教材第 6 页练习第 1 题. 5.教师引导学生回忆数集扩充过程,然后阅读教材中的相交内容,写出常用数集的记号.并让学生完成习题 1.1A 组第 1 题. 6.教师引导学生阅读教材中的相关内容,并思考.讨论下列问题: (1)要表示一个集合共有几种方式? (2)试比较自然语言.列举法和描述法在表示集合时,各自有什么特点?适用的对象是什么? (3)如何根据问题选择适当的集合表示法? 使学生弄清楚三种表示方式的优缺点和体会它们存在的必要性和适用对象。 (四)巩固深化,反馈矫正 教师投影学习: (1)用自然语言描述集合{1,3,5,7,9}; (2)用例举法表示集合 A ? {x ? N |1 ? x ? 8} (3)试选择适当的方法表示下列集合:教材第 6 页练习第 2 题. (五)归纳整理,整体认识 在师生互动中,让学生了解或体会下例问题: 1.本节课我们学习过哪些知识内容? 2.你认为学习集合有什么意义? 3.选择集合的表示法时应注意些什么? (六)承上启下,留下悬念 1.课后书面作业:第 13 页习题 1.1A 组第 4 题. 2. 元素与集合的关系有多少种?如何表示?类似地集合与集合间的关系又有多少种呢?如何表示?请同学们通 过预习教材.

streamlining. Four are standard visits, exce pt as required to participate i n traini ng, no other a ctivity. F ive is to impr ove new s reporti ng, for pr opaga nda w ork strictly accor ding to t he regulati ons . Six is strictly your prese ntation publis hed stri ctly accor ding to the regulations. 罚 济 经 或 决 理 处 好 做 权 作 操 规 违 承 对 。 明 文 与 全 安 、 度 进 督 监 并 , 宜 事 关 有 的 中 工 施 调 协 责 负 专 定 指 人 包 发

Seven is strictly thrift, required the use of vehicle s and office s pace a nd cor porate hos pitality. 3, cha nge the styl e.

Propaganda and ide ologi cal work of the new situati on and ne w requirements of the new task s, ha d done a lot of fruitful work, ha s made many achieveme nts, but further cl oser t o the grass r oots, close t o reality, clos e to the mas ses and als o ina dequate innovation must conti nue t o improve. Se cond, t he "four winds" s ome outsta ndi ng iss ues 1 , oppose formalism. One the ory is that he di dn't, wit h less close contact . The oretical st udy of consci ousnes s is not high enough, system performance i s not strong enoug h; more passive lear ning , active lear ning few generalities and learn m ore, delvi ng into le ss. E spe cially ba sed on rational thi nking on major i ssue s, applying t heory to g uide t he work done is not good enoug h, not really understa nd a nd gras p the s pirit and esse nce of the s cientific Outlook on development, did not truly achieve master y, to apply, t o a certai n extent, affect the In practical work, not your hea d, previ ous w ork experie nce, lack of innovation i nitiatives, st udy on the chara cteristics of propaganda and ide ologi cal work under the new sit uation t hr ough, grip on grassroots ideol ogical trends a nd cha nges are not dee p, to pr omote new initiatives

development and impleme ntation of ideas a nd i nitiatives. Se cond, w ork arrangements , and less s upervision. Pr opaga nda a nd i deol ogical w ork is the objective, whi ch needs t o keep the continuity efforts depl oyed, but stres sed i n the w ork time, less s upervision. For example , col or weeke nds in the summer theatrical a ctivities, city square performa nce s, urgi ng townshi ps, communitie s and rural areas shows the im plementation is i nade qua te, i ns ufficient cultural a n educational rol e to play. Thir d bas e enough, master grass-le ss real. Propaganda and i de ologi cal work i n the new situati on of char acteristics and regularity of enoug h, de ep e nough for grass -roots publi c opi nion Dynamics s urvey, for grass-r oots typi cally drive le ss. For exampl e, rural culture team a ctive, ... I'm not actively take the i nitiative to take up, the la ck of spirit of daring to, re sulting i n s ome job had a l ot of pow er, but no tangible res ults. T hird, i nnovation, la ck of motivation. Emancipati on di d not end, innovation does not exist.

and expl ore ne w methods of ideol ogical a nd cultural w ork is not much, and s ome lack of releva nce a nd timeli ness . 4, di sci pline, l oweri ng, and har d work are la cking. While worki ng and enter prising spirit dow n. No real sol ution to treat your self right, corr ectly treat past honors, their com plac ency, and w ork to see t heir scores more , less che cking his ow n s hortcomings , like to listen t o the prai se, satisfie d face, online prom otion, there are typi cal, a nd la ck of high sta ndar ds a nd stri ct requireme nts, the effect is real. Second har d drive les s. On har d and

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